>We have to stay alive, and we're all dead in less than 100 years. Therefore, we have to reproduce. Surely we also have other goals, but reproduction is a sanity check on those.

You're discounting the value of information that people can leave, separate to their DNA chain. A great many scientists, artists, philosophers, etc. bore no children. They still expressed a change in the behaviors, ideas, and lives of a great many people after them.

Actually, one might argue they are, by and large, more effective at continuity of their own goals. How many children have you seen carry on the worldviews and goals of their parents? Even throughout history?

Yes, we need SOMEONE to reproduce or there won't be anyone to read the damned work. But, the work is still there, unto itself, after it's author has passed away.

tl;dr: The production of children is not the only way affect the Universe after your death as a human.